In the standard approach the invariant amplitude \(\Pi ^{\mathrm {Phys}}(p^{2},p^{\prime 2})\)  depends on two variables \(p^{2}\)  and \(p^{\prime 2}\) ,
and the Borel transformations over \(p^{2}\)  and \(p^{\prime 2}\)  suppress
contributions of higher resonances and continuum states. The suppressed
terms afterwards can be subtracted using assumption on quark-hadron duality.
But in the soft limit even after Borel transformation besides ground-state
term \(\Pi ^{\mathrm {Phys}}(M^{2})\)  contains additional unsuppressed
contributions. This is a price to be paid in the soft approximation for
simple \(\Pi ^{\mathrm {OPE}}(p^{2})\)  expression. To remove contaminating
contributions from the phenomenological side of the sum rule, one has to act
on \(\Pi ^{\mathrm {Phys}}(M^{2})\)  by the operator [1]}, [2]}
\(\mathcal {P}(M^{2},m^{2})=\left( 1-M^{2}\frac{d}{dM^{2}}\right)M^{2}e^{m^{2}/M^{2}}, \) 
